To render this answer more generally useful, I will first give some general tests to perform not specific to your particular model of camera:

1. If the camera needs a battery, get one and pop it in. For an initial test, it needn't necessarily even be the exact same battery, as long as the voltage is close enough. (Some old cameras were designed to take batteries that are no longer manufactured, so one often has to improvise here.) Is there any corrosion in the battery compartment (bad sign)?
2. Find out if the shutter fires at all. Pressing the shutter button, do you hear the shutter closing and opening? Looking through the lens (or without lens, if the camera has interchangeable lenses), can you see the shutter close and open? (Selecting a slow shutter speed will help here.)
3. Try and figure out if the shutter speeds are sensible. A fast shutter speed (e.g. 1/500) should look and sound different from a slow one (e.g. 1/15).
4. Do all the external controls (shutter speed selector, aperture selector, ISO selector, etc.) seem to work properly?
5. Opening the back of the camera, is there visible deterioration of the light seals that keep the camera light-tight?
6. The ultimate test for an analog camera is to put some film through it and have it developed. (You don't necessarily need to get the negatives printed – just developed – to see if the results look sensible. This will be a bit cheaper.) Cameras can fail in so many ways that this really is the only way of knowing for sure whether yours is working properly.

Now, specific to your case, I'm not familiar with the Canon Autoboy, but based on a cursory web search it looks to be a fully automatic camera. This means that some of the above points will have to be modified a bit, since you won't be able for example to select a shutter speed (rather, the camera will figure out the right shutter speed for you). However, you should be able to adapt the above advice. Take the camera outdoors, thereby forcing it to select a faster shutter speed. Press the button and observe what happens. Then take it indoors (thereby forcing a slower shutter speed). Does it look and sound different? To be honest, with a fully automatic, electronic camera it's less likely that the shutter speeds will be off relative to each other, as long as the shutter fires at all.

This comes with a caveat, however. It is possible that your camera won't fire the shutter at all unless some film is loaded. If that is the case, then the above advice is, admittedly, pretty useless unless you're willing to buy a roll of film and just give it a go. Do let us know if this is the case – it would be interesting to know.

Finally, how has the camera been treated and stored? There's no reason in principle why an old camera shouldn't work if it's been properly cared for. I routinely use film cameras 50–60 years old and they perform as good as new. If this camera holds some emotional value for you, and considering that battery+film+development isn't really all that expensive, I'd give it a try!